Trump announced on Friday that the June 12 meet was back on, ending uncertainty after he cancelled it last week.
The U.S. secretary of state, who spoke with Trump on Wednesday night and with National Security Adviser John Bolton early Thursday, was accompanied by Andrew Kim, the head of a Central Intelligence Agency unit assigned to work on North Korea, and Mark Lambert, the head of the State Department's Korea desk.
Trump said he doesn't know what the letter will say but says he thinks "it'll be very positive".
He says, "The process will begin on June 12 in Singapore".
Trump said he has more sanctions he's prepared to put on North Korea, but he struck an optimistic tone about the thawing relationship, partially evidenced by the fact that Kim Yong Chol is the highest-ranking North Korean official to visit the U.S.in 18 years. Two more meetings are scheduled for Thursday.
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Analysts say that depends on whether still- formidable hurdles can be overcome.
The Trump administration has pressed for the North to rapidly takes steps to turn over its nuclear program, while Pyongyang has said it expects a slower, step-by-step process in which the North receives reciprocal benefits, including economic incentives. He doesn't plan to introduce new sanctions.
Kim's government said it would never give up all its nuclear weapons, calling them essential to the regime's security, one of the claims that led to Trump's cancellation last week.
Trump talked to reporters after escorting Kim out of the Oval Office and posing for photos, along with Pompeo, before Kim's departure.
The letter from Kim Jong Un had to first be inspected by United States officials before it was delivered to the president, a White House official confirmed.
Pompeo's meetings in New York City included Kim Yong Chul, the top aide who will carry Kim Jong Un's letter to Washington.
According to KCNA, Mr Assad said: "The world welcomes the remarkable events in the Korean Peninsula brought about recently by the outstanding political calibre and wise leadership of Kim Jong Un".